Mathematics or Applied Mathematics

A degree in mathematics is useful for those seeking careers in teaching, research, the sciences, or business and government. The traditional mathematics major is particularly appropriate if students plan to teach or enter professional school, or if they seek an interesting major within the liberal arts. The applied mathematics major is suggested if a student plans a career in actuarial work, industrial mathematics or statistics.

The minor in mathematics consists of 21 units of required course work. Please refer to the Degree Requirements section for more information.

In addition to the required courses, students should select relevant courses in the social and physical sciences to complement and augment their major.

Traditional Mathematics Major Requirements

Mathematics majors should take Math 3101 Foundations for Higher Mathematics as one of these courses. In addition to the calculus sequence and Math 3101, 15 units of 300- and 400-level courses must be completed successfully.

An introductory course for students with little or no programming experience. Topics include the software development process, documentation, debugging, and testing within the commonly used Python environment. At the end of the course students should be able to write and debug basic programs to display and interpret data using accepted programming conventions and styles.

Continuation of U20 155, starting with a brief review of definitions and formulas. The concept of the integral; the Fundamental Theorem of Calculus; techniques of integration; application of the integral including areas, volume, and work; differential and integral calculus with elementary transcendental functions. Prerequisite: U20 155 or equivalent.

This is a first course in statistics with examples and applications from a variety of disciplines, and emphasis on the social, behavioral and natural sciences. Students will learn about key topics and statistical methods that may be applied to areas such as economics, mathematics, psychology, business, and health sciences, to name a few. The course will provide a foundation in descriptive and inferential statistics, and in probability. Students will learn numerical and graphical methods of describing data and will study some of the more common distributions. Topics to be covered include hypothesis testing, confidence-interval estimation, correlation, regression, analysis of variance, contingency tables, quality control, and nonparametric statistics. This course may be applied to University College majors in economics, managerial economics, and political science. Students must have access to the internet, have an email account, and have some familiarity with Microsoft Excel to take the course. Prerequisite: College Algebra.

Mathematics plays an important role in society, from engineering to architecture to the social and behavioral sciences. This course will expose non-math majors to fascinating sides of mathematics that are typically not discussed in standard math courses. Students will learn effective thinking techniques with applications beyond standard mathematics, and discover exciting ideas and new perspectives about the world. We will look at questions like: What do rabbits, piano keyboards, and pine cones have to do with the Parthenon? What do secret codes and bar codes have to do with number systems and prime numbers? What are some uses and misuses of mathematics in everyday life? Why are coincidences not so amazing after all? Prerequisite: proficiency in high school algebra.

Visual representations of data are important for conveying complex information simply. There are many packages available in R (such as ggplot2) that can be used to generate plots and graphs of various kinds. Sometimes the default output from a particular command is not the best way to communicate a particular result or trend. This course will help students to learn more about the common ways to display data, as well as how to make changes to the codes so that the visualizations are more effective. Visualization techniques involve study from areas such as graphic design, computer science, psychology, and mathematics. Topics include: categorical data, distributions, time series, scatter plots, and maps. Prerequisites: Math 124 and Math 205 or 305 or equivalents.

Continuation of Math 233 emphasizing topics of interest in the physical sciences. Topics in multivariable and vector calculus (div, grad, curl); line, surface integrals and connections to electromagnetism; Fourier series and integrals; boundary value problems (diffusion and wave equations); additional topics if time permits. Students may not receive credit toward a math major or minor for both Math 308 and Math 318. Prerequisites: Math 233 and 217, or permission of instructor.Same as L24 Math 308

Detailed treatment of the algebra of matrices. Rank and equivalence of matrices. Matrices over a number field. Linear equations and linear dependence. Determinants. Prerequisite: U20 256 or equivalent.

Introduction to the rigorous techniques used in more advanced mathematics. Topics include propositional logic, use of quantifiers, set theory, methods of proof and disproof (counterexamples), foundations of mathematics. Use of these tools in the construction of number systems, and in other areas such as elementary number theory, combinatorial arguments, and elementary proofs in analysis. Prerequisite: Math 256 or permission of the instructor.

A first course in the design and analysis of experiments, from the point of view of regression. Factorial, randomized block, split-plot, Latin square, and similar design. Prerequisite: CSE 131 or 200, Math 3200, or permission of instructor.Same as U20 Math 520

Life table analysis and testing, mortality and failure rates, Kaplan-Meier or product-limit estimators, hypothesis testing and estimation in the presence of random arrivals and departures, and the Cox proportional hazards model. Techniques of survival analysis are used in medical research, industrial planning and the insurance industry. Prerequisites: CSE 131 or 200, Math 309 and 3200, or permission of the instructor.Same as L24 Math 434

Theory and practice of linear regression, analysis of variance (ANOVA) and their extensions, including testing, estimation, confidence interval procedures, modeling, regression diagnostics and plots, polynomial regression, colinearity and confounding, model selection, geometry of least squares, etc. The theory will be approached mainly from the frequentist perspective, and use of the computer (mostly R) to analyze data will be emphasized. Prerequisites: CSE 131 or 200, Math 3200 and a course in linear algebra (such as Math 309 or 429), or permission of instructor.Same as L24 Math 439

Theory of estimation, minimum variance and unbiased estimators, maximum likelihood theory, Bayesian estimation, prior and posterior distributions, confidence intervals for general estimators, standard estimators and distributions such as the Student-t and F-distribution from a more advanced viewpoint, hypothesis testing, the Neymann-Pearson Lemma (about best possible tests), linear models, and other topics as time permits.Same as U20 Math 594

Content varies with each offering of the course. Past offerings have included such topics as random walks, Markov chains, Gaussian processes, empirical processes, Markov jump processes, and a short introduction to martingales, Brownian motion and stochastic integrals. Prerequisites: Math 318 and 493, or permission of instructor.Same as L24 Math 495